Connecting mathematics and mathematics education : [electronic resource] collected papers on mathematics education as a design science / Erich Christian Wittmann.

Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25-36 -- 2. Clinical Interviews Embedded in the "Philosophy of Teaching Units" -- A Means of Developing Teachers' Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18-31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291-308 -- 4. Mathematics Education as a 'Design Science'. Educational Studies in Mathematics 29 (1995), 355-374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 -- 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97-165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1-20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 -- 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 -- 232) (transl. from German) -- 11. Structure genetic didactical analyses -- empirical research "of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 -- 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science -- Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1- 20.

This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the "design science conception" has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.